Yield Calculations for Treasury Bills William L. Silber
Yield Calculations for Treasury Bills
William L. Silber
Question
Suppose you could buy a 91-day T-bill at an asked price of $98 per $100 face value and you could sell to the dealer at a bid price of $97.95 per $100 face value. What are the quotation conventions on this bill and how is the yield calculated? What is the best measure of the yield on a T-bill?
Answer
1) This T-bill would be listed in a table as follows:
Days to Maturity 91
Bid 8.11
Ask 7.91
Ask Yield 8.186
2) The ask yield in the last column is the bond yield equivalent (b.y.e) of this T-bill. This is the yield (assuming simple interest) if you bought the bill at the ask price of 98 per 100 face value and held it for the full 91 days.
B.Y .E.
=
?? ?
F
P
P
?? ?
/
t
F = Face Value (=$100) P = Price Paid t = Fraction of a year
In our case,
( ) B.Y
.E.
=
100 98
98
/
91 365
= .08186 = 8.186%
NB: This formula is simple interest because it comes from: P(1+ rt ) = F
which can be solved for r as
r
=
?? ?
F
P
P
?? / t ?
3. The 7.91 under the word Ask in the table comes from the discount rate calculated on the bill. The discount rate is defined as:
( ) discount
rate
=
?? F ?
-P F
?? / ?
x 360
where X = days to maturity
In our case (using the ask price):
( ) (ask
)
discount
rate
=
?? 100 - 98 ? 100
?? ?
/
91 360
= .0791 = 7.91%
4) The 8.11 in the table under the word bid uses the same discount rate calculation as above except it uses the bid price (=97.95) in the formula
( ) (bid
)
discount
rate
=
?? ?
100 - 97.95 100
?? ?
/
91 360
= .0811 = 8.11%
5) Note that the (ask) discount rate will always be lower than the ask yield based on the b.y.e. formula because F appears in the denominator of the discount rate formula while P is in the denominator of the b.y.e. formula (and F>P as long as yields are positive). In addition, 360 ................
................
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